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Title: GR8677.035
Post by: conantee on January 02, 2010, 06:52:15 AM
Question 34-36
The potential energy of a body constrained to move on a straight line is kx^4 where k is a constant. The position of the body is x, its speed v, its linear momentum p, and its mass m.

35. The Hamiltonian function for this system is
(A) \frac{p^2}{2m} + kx^4
(B) \frac{p^2}{2m} - kx^4
(C) kx^4
(D) \frac{1}{2}mv^2 - kx^4
(E) \frac{1}{2}mv^2



Title: Re: GR8677.035
Post by: conantee on January 02, 2010, 07:05:51 AM
If you don't have anything about Hamiltonian, you can still guess that (C) and (E) are too plain. They are wrong.

Then, (B) and (D) are the same thing except (B) uses momentum while (D) uses velocity. Now, you may recognize that Hamiltonian is written is terms of generalized coordinates and conjugated momentum, so (D) is wrong.

Make a guess, or if you remember Hamiltonian now, you get (A) as the answer. (Hamiltonian is equivalent to totally energy)

The correct answer is (A). 73 of 100 people got it correctly.